Question

look at this diagram: if \\( \overleftrightarrow{mo} \\) and \\( \overleftrightarrow{pr} \\) are parallel lines and \\( m\angle pqs = 60 ^ { \circ } \\), what is \\( m\angle pqn? \\)

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight line sum to \(180^{\circ}\).
\(m\angle PQS + m\angle PQN=180^{\circ}\)

Step2: Substitute the given value

Given \(m\angle PQS = 60^{\circ}\), then \(60^{\circ}+m\angle PQN = 180^{\circ}\)

Step3: Solve for \(m\angle PQN\)

\(m\angle PQN=180^{\circ}- 60^{\circ}\)

Answer:

\(120\)